Reality consists of 3 spatial dimensions with time adding a fourth dimension. But what reason could we possibly have for putting such limits on reality? Do higher dimensions have any reality apart from their construction within a mathematical framework?
Plato believed in the reality of higher dimensions, as his allegory of the cave demonstrated. Claude Bragdon considered the fourth dimension to be spatial. He believed our conception of time as the fourth dimension was mistaken. We experience time as a “fourth dimension” because of our lack of ability in sensing this dimension which is spatial. He used an analogy equivalent to Plato’s cave analogy. A flatlander would experience a cube travelling through its plane-wise world as beginning with a point, expanding to a polygon and finally contracting to a point before disappearing from sight. It is obvious to me that this flatlander inhabits a three dimensional world and is itself three dimensional, but can only perceive in two spatial dimensions. It perceives itself and its fellow flatlanders as a polygon which changes over time. It conceives of reality as consisting in two spatial dimensions and one time dimension.
Rudolf Steiner discusses the dimensions of space and beyond in a collection of lectures and discussions collated in the book, “The Fourth Dimension. Sacred Geometry, Alchemy, and Mathematics.”
Here he considers beings consisting of various dimensions. A being of two spatial dimensions would only be capable of perceiving one dimension, a being of three dimensions would only perceive two dimensions and so on. In this resect we are beings of four spatial dimensions but we only perceive three of them. Although each of these three dimensions are unique. They all differ experientially.
Regarding the contemplation of the fourth dimension, Steiner admired the work of Charles Howard Hinton who has been credited with coining the word “tesseract” as the name for the four dimensional equivalent to the cube. As a cube can be represented in two dimensions by the hexagon, so the tesseract can be represented in three dimensions by the rhombic dodecahedron.
In Steiner’s lectures linked to above, he introduces his audience to the mathematical treatment of the higher dimension with accompanying diagrams. He also highlights the differences between mathematical treatment and the reality of further dimensions. He does not view reality as consisting of a series of ever increasing spatial dimensions. The neutralization of polarity in one dimension gives rise to the adjacent dimension. For example when two planes cross there arises a line. The planes give rise to the line but the line has no two-dimensional component.
He considers us to be six-dimensional beings with the three physical dimensions being a reflection of three higher causal, creative dimensions. The plants we perceive are three dimensional images of four dimensional beings. In his “archetypal plant” Goethe caught a glimpse of the reality of plants as four-dimensional beings.
Time is a projection of the fourth dimension into the three spatial dimensions of the physical world. It is a feature of living beings that they change intrinsically over time. Sentient beings encompass five dimensions and self aware beings encompass six dimensions. Thinking is dimensionless.
Now when we try to understand the connection between mind and matter some people regard this as a problem of interaction between an immaterial mind and a material body. This becomes a problem for both materialists and idealists to grapple with. But if we look at this from the point of dimensions we can see a solution. We can take an example of a similar problem in two-dimensional reality. In this two-dimensional world we can imagine a ring with a smaller disc sitting outside it. How can the disc get inside the ring without somehow interfering with the structure of the ring? This would be impossible if reality was limited to two dimensions. But if the disc could be lifted into the third dimension and then moved into the ring, this would seem like a miracle to any being perceiving in just two dimensions. It would be as if the disc disappeared and then reappeared within the ring. It is the same with an act of willing a part of my body to move, i.e. mind affecting matter. The connection does not occur in our familiar three dimensional spatial world but in the higher dimensions in which my inner sentient life belongs. This activity impinges on the three-dimensional world but it is not restrained by it.